Ponder This

June 2013

Find a rational number (a fraction of two integers) that satisfies the following conditions:

Its denominator is five digits long and all of them are different.

In the infinite decimal representation, every digit occurs an equal number of times in the digits from one billion to two billion places to the right of the decimal point (inclusive), except for the last digit in the denominator, which occurs twice as often as the other nine digits.

Its numerator contains as few different digits as possible.

Update 6/4: To clarify the problem, here is an example: 5/17 = 0.294117647058823529411764705882... and in the 11 digit in the places 20-30 after the decimal point the digit 7 (the last digit of the demonimator) appears twice as many times as the digit 4, but not twice as many as the digit 9 (which does not appear there at all).

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to:ponder@il.ibm.com